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Mac Rowe doesn't sweat the petty stuff.In fact, he just cannot detect small differences.He consumes two goods, x and y.He prefers the bundle (x, y)to the bundle (x', y')if and only if (xy x'y' 1).Otherwise he is indifferent between the two bundles.
a.Show that the relation of indifference is not transitive for Mac.(Hint: Give an example.)
b.Show that the preferred relation is transitive for Mac.
On Jun 06, 2024
a.Consider the bundles A (1, 1), B (1, 1.75), and C (1, 2.5).Then A is indifferent to B and B to C, but C is preferred to A.
b.To see that strict preference is transitive, suppose we have any three bundles, (x, y), (x', y')and (x'', y'').If the first is preferred to the second and the second to the third, then xy x'y' 1 and x'y' x''y'' 1.Simple algebra shows that xy x''y'' 1.Therefore the first must be preferred to the third.